TY - JOUR

T1 - Prime divisors in Beatty sequences

AU - Banks, William D.

AU - Shparlinski, Igor E.

PY - 2007/4

Y1 - 2007/4

N2 - We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence ⌊ α n + β ⌋, n = 1, 2, ..., where α, β ∈ R, and α > 0 is irrational. For example, we show thatunder(∑, n ≤ N) ω (⌊ α n + β ⌋) ∼ N log log N and under(∑, n ≤ N) (- 1)Ω (⌊ α n + β ⌋) = o (N), where Ω (k) and ω (k) denote the number of prime divisors of an integer k ≠ 0 counted with and without multiplicities, respectively.

AB - We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence ⌊ α n + β ⌋, n = 1, 2, ..., where α, β ∈ R, and α > 0 is irrational. For example, we show thatunder(∑, n ≤ N) ω (⌊ α n + β ⌋) ∼ N log log N and under(∑, n ≤ N) (- 1)Ω (⌊ α n + β ⌋) = o (N), where Ω (k) and ω (k) denote the number of prime divisors of an integer k ≠ 0 counted with and without multiplicities, respectively.

UR - http://www.scopus.com/inward/record.url?scp=33846867490&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2006.07.011

DO - 10.1016/j.jnt.2006.07.011

M3 - Article

AN - SCOPUS:33846867490

VL - 123

SP - 413

EP - 425

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 2

ER -